LPG quantity calculation from liquid density
ADM003GVAE1005 303
Step 5
The conversion of corrected liquid level to liquid volume is carried out using stored
values of key level/volume data points for the tank, with Lagrange cubic
interpolation between. The calculation for liquid value (VL) is defined in Spherical
Tanks in the Strap Table Volume section, earlier in this chapter. For the LPG
calculation method the corrected level value HC is used in the conversion of level
to liquid volume.
Step 6
Liquid volume needs to be corrected for the thermal expansion of the tank shell.
The nature of the correction depends upon the type of tank.
Thermal correction
Where αT = coefficient of thermal expansion of tank /°C
For a vertical cylinder:
for a horizontal cylinder:
for a sphere:
A pressure correction should be applied. This will take into account the vapor
space pressure and the hydrostatic head of liquid. The average pressure
throughout the sphere is assumed to be one half the total liquid level, converted to
a pressure, plus the vapor space pressure. The linear stress, is then calculated
and this used, with Youngs modulus, to calculate the increase in radius. The F
factor necessary for temperature correction is again used to convert change in
radius to change in liquid volume.
The units of Youngs modulus are generally known in bar. The units of length used
in the calculation of stress do not matter, but the pressure must be in bar, to match
the units of Youngs modulus. The following equations are based upon the use of
bar for Youngs modulus. Note the P is in bar g and HC is in mm. Calculate
average pressure as:
F = 2
F = 1 + 2 (A - sin A)/(A - sin A cos A)
where HC = liquid depth (corrected)
R = cylinder radius
F = HC
2
R/(HC
2
r - HC
3
/3)
where H = liquid depth
R = cylinder radius
PAV = P + DENL x HC/2.04 x 10
7
CF αTTL 15–()=
Acos=
1–
1
HC
R
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